The National Football League appears to be bucking the Obama administration's request to help promote the health care overhaul, as Republican lawmakers pressure all the major sports leagues not to get involved in the effort.

In a statement obtained by Fox News, an NFL spokesman said the league has "no plans to engage in this area and (has) had no substantive contact with the administration" about the implementation.

Earlier in the week, Health and Human Services Department officials said they were talking to the NFL, NBA and others about possible advertising campaigns, in the run-up to the launch of a key part of the health care law.

But Senate Republican Leader Mitch McConnell, R-Ky., and Sen. John Cornyn, R-Texas, on Friday wrote to the heads of six professional sports organizations urging them not to take the bait.

"Given the divisiveness and persistent unpopularity of the (health care law), it is difficult to understand why an organization like yours would risk damaging its inclusive and apolitical brand by lending its name to its promotion," they wrote.

The senators suggested the administration was reaching out to them because the law is so "unpopular."

The NFL's statement late Friday was in response to lawmakers' concerns.

The letters were sent to the heads of the NFL, Major League Baseball, National Basketball Association, National Hockey League, Professional Golf Association and NASCAR.

Republicans, who have been largely opposed to the law ever since they tried to kill the legislation back in 2009 and 2010, have in recent months tried to rein in the administration's promotional efforts.

Several GOP lawmakers want investigations into HHS Secretary Kathleen Sebelius' effort to solicit support from private groups for a non-profit that is promoting the law.

Some of the biggest elements of the health care law are expected to take effect by early 2014. This fall, enrollment begins for a new marketplace -- called exchanges -- of government-regulated insurance plans. The requirement that nearly everyone buy health insurance kicks in at the beginning of 2014.

Despite the controversy over the possibility of the government partnering with sports leagues, this wouldn't be the first occasion the two have linked up.

The military has long engaged in sponsorships with NASCAR, though that relationship encountered hurdles in this age of fiscal austerity. The Army recently decided to drop its sponsorship, though the Air Force did not follow suit.